Simplify cube root of x^2* sixth root of x^5

$\sqrt[3]{x^{2}} \cdot \sqrt[6]{x^{5}}$

Multiply $\sqrt[3]{x^{2}} \sqrt[6]{x^{5}}$ .

Rewrite the expression using the least common index of $6$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$x^{\frac{2}{3}} \sqrt[6]{x^{5}}$

Rewrite $x^{\frac{2}{3}}$ as $x^{\frac{4}{6}}$ .

$x^{\frac{4}{6}} \sqrt[6]{x^{5}}$

Rewrite $x^{\frac{4}{6}}$ as $\sqrt[6]{x^{4}}$ .

$\sqrt[6]{x^{4}} \sqrt[6]{x^{5}}$

Combine using the product rule for radicals.

$\sqrt[6]{x^{4} x^{5}}$

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[6]{x^{4 + 5}}$

Add $4$ and $5$ .

$\sqrt[6]{x^{9}}$

Factor out $x^{6}$ .

$\sqrt[6]{x^{6} x^{3}}$

Pull terms out from under the radical.

$x \sqrt[6]{x^{3}}$

Rewrite $\sqrt[6]{x^{3}}$ as $\sqrt{\sqrt[3]{x^{3}}}$ .

$x \sqrt{\sqrt[3]{x^{3}}}$

Pull terms out from under the radical, assuming real numbers.

$x \sqrt{x}$